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Question

Solve each problem using two variables and a system of two equations. Solve the system by the method of your choice. Note that some of these problems lead to dependent or inconsistent systems.
On Monday the office staff paid a total of S7.77 including tax for 3 coffees and 7 muffins. On Tuesday the bill was $\$ 14.80$ including tax for 6 coffees and 14 muffins. If the sales tax rate is $7 \%,$ then what is the price of a coffee and what is the price of a muffin?

Joshua Eastwood · Accepted Answer

with the price of coffee and muffins. So coffee is gonna be the price. R C sword is getting praise of coffee, and then the muffins will call em. And what it tells us is that on Monday, three coffees and seven muffins was a total of $7.77 including tax. Okay, And then the second day on Tuesday, it says it was six coffees and 14 muffins, and the cost was $14.80. So what I notice is when I multiply this by two, I get six coffees and 14 muffins is $14. But then more than that, because of the 77 cents Oh, actually, I&#x27;m up like 7 77 like Look at 15 54. And this says that six C plus 14 m is actually equal to 14 80. And so what we have is an inconsistent system. It&#x27;s not possible that the coffee and muffins, the same number coffees and the same number of muffins added together give you two different values from the same place. It&#x27;s inconsistent, which means there&#x27;s no solution

Julie Silva · Answer

So in this problem, we&#x27;re told about two trips to it. Sounds like a coffee shop that aren&#x27;t you made. And so what we&#x27;re trying to figure out is to cost for one donut and one coffee. So I&#x27;m gonna let d represent the cost for a donut, and I&#x27;m going to let see represent the cost for coffee. And so what we&#x27;re gonna do in this type of problem is working a write an equation for each day. So on Monday, we&#x27;re told that he spent a total of $3.40. So when we add up what he spent on doughnuts and coffee, that&#x27;s what it should equal. Well, we&#x27;re told he got three doughnuts, but the cost for a donut is D. So three D will represent the cost for the doughnut. And he got two coffees. So when we add to see to that, that would be the cost for the coffee. So now we&#x27;ve run in an equation for Monday. We&#x27;re gonna do the same thing for Tuesday. One Tuesday, we&#x27;re told he spent a total of $3.60 and he bought two doughnuts and three coffees. So two D plus three c will equal $3.60. And now we just have to solve the system of equation. I&#x27;m going to do this using the addition. Nothing. I know that&#x27;s nothing. Cancels right away. So I&#x27;m gonna look at my devalues. So I&#x27;m going to multiply the first equation by negative two and the second equation by three. So when I multiply that first equation by negative to, I&#x27;m gonna get negative 60 minus foresee and negative two times $3.40 would be negative $6.80. Now I&#x27;m gonna multiply in the next equation by three. I&#x27;m gonna make it red just so we have a little bit of a difference there. Well, three times to D is 60 three times three c is positive nine c and three times $3.60 will give us $10.80. Now we can add the two equations up because negative 60 plus 60 0 cancels and then we have negative foresee plus nine C, which is five C and negative. $6.80 plus $10. 80 cents is just $4. So to get, see we&#x27;re gonna divide both sides by five now because we&#x27;re representing money. We want to actually write this as a decimal. And 4/5 is the same as 0.80 in other words, 80 cents. So now we know the cost for coffee. It&#x27;s 80 cents, but we now we need to cost for the doughnut. So we&#x27;re gonna pick even the first or second equation. I&#x27;ll use the first equation, so we have three D plus to see is $3.40 and we&#x27;re gonna substitute 80 cents in for C. So we&#x27;ll have three D plus two times 80 cents equals $3.40. Well, two times 80 cents is a dollar 60. So we have three D plus a dollar, 60 equals $3.40. So we&#x27;re in the subtracted dollar, 60 from both sides, so three D will be equal to a dollar 80 and then we&#x27;re gonna divide both sides by three. And what we find is we get 60 cents and now we&#x27;ve found the cost for the doughnut is 60 cents, and now we found both the cost of the doughnut and the cost

Wesley Hines · Answer

So for this problem, we&#x27;re just flat out given three systems based off the price of three different orders. So going to have X represent milk I&#x27;m going to have. Why represent coffee Copely and C represents doughnuts. You just right that little better daamoth. And so we&#x27;re given for Hector that three X plus four. Why a seven Z is equal to 5 45 and then for, um, the order on Tuesday were given that four X plus two y plus Beat Z is equal to 5 30 and then on Wednesday were given that two x plus find why I lost six. C is equal to 5 15 And then essentially, we&#x27;re trying to, um, calculates the order are the pricey order on Thursday were asked if someone orders five X to why and nine Z Um, how much change will they get back on a $10 bills? So I&#x27;ll put this I&#x27;m gonna put this weirdly just so it how it works mathematically, but you don&#x27;t have to think or write this in terms of this problem. So we&#x27;ll say that this is equal to W and that the answer our problem is what is 10 minus W. Okay, so now we&#x27;re looking to eliminates, um X from two of our equations so that we can use substitution to solve for a variable. And the first thing I&#x27;m going to do for this is going to multiply Equation three by early March, our equations first. So we have equation one equation to in equation three. I&#x27;m going to multiply equation three by negative too. And then, uh, add that to equation to use a two plus negative two times three. And the reason I&#x27;m doing that as biz will cancel the Xer&#x27;s. And then I&#x27;m gonna do the something similar for equation one to kill. So, uh, cancel the other ex. So when I do this, I&#x27;m going tohave for X plus two y plus eight z, uh, minus four X minus 10. Why? Minus 12 z That is going to be equal to 5.3 minus 10.3. And so I&#x27;ll be left with negative eight y minus for Z is equal to negative five. And then I&#x27;m going to multiply equation one by, um, negative too. And equation three by three that both have an extreme of six and I can subtract that way. Um, doing the same promises as earlier. This will give that seven Y plus four z is equal to 4.55 So now we have two equations in terms of Y and Z. I&#x27;m going to use substitution to solve for why and then necessary sell frizzy and then substitute to solve for y. So let&#x27;s mark this as equation for and equation five. So if I solve for Y from equation for Ah So I saw Rosie o get that Z is equal to 1.25 minus two. Why? I&#x27;m gonna substitute this into Equation five right there. Andi, this will give that why is equal 2.0 point 450.45 That&#x27;s right. That little bit 0.44 and then from here, since Z is equal to 1.25 minus two. Why I can substitute 0.45 back in this would be 1.25 minus point line which would get that Z is equal 2.35 And now that we have the value of coffee and donuts weaken, use the&#x27;s in any of the three original equations given to solve for X doing this will yield that X is equal to 40 cents. And now that we have the values of X, Y and Z, we are to plug Hm and to this equation up here because this is the equation we&#x27;re going to use to solve for our answer. And when we do this will know that the price of the final order is 605 So W is equal to 605 We know that our answer is 10 minus w 10 minus w is 3 95 So on the order on Thursday, there change will be $3.95.

Joshua Eastwood · Answer

that shit is gonna ask us about the price for two different types of books paperbacks and hard backs. And it sells a 10. You got six paperbacks and three hardbacks for 8 25 So what I&#x27;m gonna do is I&#x27;m just gonna let each be the hardbacks praise for the hardbacks. And then he is gonna be the price for the paperbacks. So if we make that statement again Tan, you got six paperbacks. That means she got six p&#x27;s. And then she got three hardbacks, so that&#x27;s three ages. And she paid $8.25. Okay? And then it tells us that Greta I got four paperbacks and five hardbacks for 9 25 So she got it for 9 25 And again, it&#x27;s four haber and five hard backs of four paper and five hardbacks. Right? And we&#x27;re asked to solve this. So what I&#x27;m gonna do, I&#x27;m actually just gonna multiply this by two, and I&#x27;m gonna multiply this by three. And the reason I&#x27;m gonna do that is because then I can solve this by edition or elimination, so I&#x27;m gonna get 12 p plus six age is equal to eight. Sorry, Not 8 25 anymore. 16. 50. And then I&#x27;m gonna multiply this one by three. So 12 p plus 15 h it is going to equal 27 75 and then I&#x27;m simply going to subtract thes equation. So I&#x27;m gonna get six minus 15 which is minus nine each and 16 50 minus 27 75 is minus 11 25. So that means that age is 11. 25 divided by nine negatives. But they cancel. All right? And that&#x27;s going to give me. I take it like a calculator, and I would encourage you to the same. Just take a calculator and do it on your calculator, making sure that you&#x27;re getting the same answer that I am. Hearn Backstrom. Oh, to a dollar 25. So hurt by backs costs a dollar. 25. We need paperbacks. So six pee. I&#x27;m just gonna put it back into this equation. Okay, so that means it&#x27;s six p plus three times a dollar 25 is gonna equal 8 25 So we get six p plus 3 75 is a 25 and I&#x27;m gonna run out of room, so I&#x27;m just gonna jump to the next page. That means at six p is 8.25 minus 3.75 So six p is gonna be 4 50 And if you divide for 50 by six. 75 cents So paperbacks cost 75 cents. Hardbacks are dollar. 25 paperbacks are 75 cents. It&#x27;s gonna make sense because paperbacks are usually easier to produce. That&#x27;s my

Whitney Dillinger · Answer

for this problem. We&#x27;re looking at the prices of cappuccinos in long days at a Panera Bread. So we&#x27;re going ex br cappuccinos and I&#x27;m abbreviate that And why is gonna be our lot tastes abbreviate that when we want to find the price of each were giving some information. We are told that two cappuccinos, so to eggs plus three LA tests or three why equals a total of $14 and 55 cents. We&#x27;re also toe that one cappuccino and to our Tae&#x27;s equals a total of $8.77. So I wrote both of the information into an equation form. And so now we can use those to solve. So let&#x27;s start with this second equation. X plus two y equals $8.77. We can solve for X by subtracting, too. Why on both sides, so X will equal negative two y plus eight 0.77. So now that we know what exes, we can plug it into his first equation. So we&#x27;ll have to times negative two y plus 8 77 plus three y will equal $14.55. So I have distributive property Negative for why I was 17. 54 plus three y well, equal. $14.55. I combined my wise negative for wine. Three. Why get negative? Why so negative? Y plus 17 54 will equal 14. 55. We&#x27;re gonna subtract 17 54 on both sides. So negative y equals negative $2.9 Nonsense. I don&#x27;t want a negative. Why someone go ahead and divide by negative one. So why will equal $2.9 on sent? So the cost of a lot is $2 and 19 on six. So now that we know that let&#x27;s fund the price of a cappuccino well, we know a cappuccino is negative Two times two a lot A or why plus 8 77 So that means that a cappuccino is negative two times 299 plus 8 77 So X would equal negative $5.98 plus $8.77. So X is gonna equal $2.79. So the cappuccinos cost is $2.79

Joshua Eastwood · Answer

but the question were given is about a hotel that is renting double rooms and single rooms. So I&#x27;m gonna call them D and s. It says that the double room costs 20 more dollars than a single room. So that means that the double room is the price of the single room plus 20. And the second part says that they made $3949 and they did it when they rented 15 doubles and 26 singles. So 15 d plus 26 s. But what I do isn&#x27;t going to solve this, and I&#x27;m gonna use substitution. I&#x27;m just gonna substitute that into the second equation, so I&#x27;m gonna get 3949 is equal to 15 times, and then instead of D, I&#x27;m gonna put ask Boss 20 and then plus 26 s. So I get 3949 is equal to 15 times s waas 20 times 15 and then plus 26 s. So we bring this $300 over there, I&#x27;m gonna get 3000 subtracted from Just attracted 300,003,649 is equal to 15 plus 26 which is 41. Yes, So then s is equal to whatever 36 49 divided by 41 is. So if I take 36 49 divided by 41 I get $89 for a single room, costs $89 of a single room costs $89 in a double room. That&#x27;s 100 and $9. Because it&#x27;s just s plus 20 Ijust add 20 to that.

Problem

Solve each problem using two variables and a syst…

Problem 71 Hard Difficulty

Answer

Inconsistent, no solution

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Inconsistent, no solution

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Precalculus Functions and Graphs